An Introduction to Minimax Theorems and Their Applications to Differential Equations (Hardcover)

Maria do Rosario Grossinho

ISBN 10: 0792368320 / ISBN 13: 9780792368328

Editore: Kluwer Academic Publishers, Dordrecht, 2001

Riguardo questo articolo

Hardcover. This text is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: to present a survey of existing minimax theorems; to give applications to elliptic differential equations in bounded domains; to consider the dual variational method for problems with continuous and discontinuous nonlinearities; to present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities; and to study homoclinic solutions of differential equations via the variational methods. This text is intended to be an introduction to critical point theory and its applications to differential equations. Its goals include: presenting a survey of existing minimax theorems; and giving applications to elliptic differential equations in bounded domains. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780792368328

Dati bibliografici

• Titolo: An Introduction to Minimax Theorems and Their Applications to Differential Equations (Hardcover)
• Editore: Kluwer Academic Publishers, Dordrecht
• Data di pubblicazione: 2001
• Lingua: Inglese
• ISBN 10: 0792368320
• ISBN 13: 9780792368328
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

This text is meant to be an introduction to critical point theory and its ap- plications to differential equations. It is designed for graduate and postgrad- uate students as well as for specialists in the fields of differential equations, variational methods and optimization. Although related material can be the treatment here has the following main purposes: found in other books, * To present a survey on existing minimax theorems, * To give applications to elliptic differential equations in bounded do- mains and periodic second-order ordinary differential equations, * To consider the dual variational method for problems with continuous and discontinuous nonlinearities, * To present some elements of critical point theory for locally Lipschitz functionals and to give applications to fourth-order differential equa- tions with discontinuous nonlinearities, * To study homo clinic solutions of differential equations via the varia- tional method. The Contents of the book consist of seven chapters, each one divided into several sections. A bibliography is attached to the end of each chapter. In Chapter I, we present minimization theorems and the mountain-pass theorem of Ambrosetti-Rabinowitz and some of its extensions. The con- cept of differentiability of mappings in Banach spaces, the Fnkhet's and Gateaux derivatives, second-order derivatives and general minimization the- orems, variational principles of Ekeland [EkI] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais-Smale conditions and mountain-pass theorems are consid- ered.

Contenuti

Preface. 1. Minimization and Mountain-Pass Theorems. 2. Saddle-Point and Linking Theorems. 3. Applications to Elliptic Problems in Bounded Domains. 4. Periodic Solutions for Some Second-Order Differential Equations. 5. Dual Variational Method and Applications. 6. Minimax Theorems for Locally Lipschitz Functionals and Applications. 7. Homoclinic Solutions of Differential Equations. Notations. Index.